The Stone representation theorem states that every Boolean algebra is isomorphic to the Boolean algebra of clopen subsets of a compact totally disconnected T2-space. The representing space can be taken to be the Stone space of ultrafilters of the Boolean algebra.
Stone Representation Theorem
See also
Boolean Algebra, Clopen, Stone Space, UltrafilterExplore with Wolfram|Alpha
References
Halmos, P. Lectures on Boolean Algebras. Princeton, NJ: Van Nostrand, 1963.Cite this as:
Weisstein, Eric W. "Stone Representation Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StoneRepresentationTheorem.html